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(p+5)/8 and (p+1)/4 = Prime Numbers (Posted on 2010-04-12) Difficulty: 2 of 5
Determine all possible value(s) of a prime number p such that each of (p+5)/8 and (p+1)/4 is a prime number.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Some Thoughts computer exploration (spoilers) | Comment 1 of 5
list
    5   P=1
   10   while P>0
   20       P=nxtprm(P)
   30       P1=(P+5)//8:P2=(P+1)//4
   40       if P1=int(P1) and P2=int(P2) then
   50             :if prmdiv(P1)=P1 and prmdiv(P2)=P2 then
   60                 :print P;P1;P2
   70   wend
OK
run
 3  1  1
 11  2  3
 19  3  5
Break in 20
?p
 485582459
OK

so it would seem that 3, 11 and 19 are the only values. They are definitely the only values lower than 485,582,459.


  Posted by Charlie on 2010-04-12 12:27:00
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